1 Introduction ................................................ 5
2 Right-topological semigroups ................................ 6
3 Acts and their endomorphism monoids ......................... 8
4 The function representation of the semigroup P2(X) ......... 11
5 Twin and I-twin subsets of groups .......................... 16
6 Twinic groups .............................................. 18
7 2-Cogroups ................................................. 22
8 The characteristic group H{K) of a 2-cogroup К ............. 25
9 Twin-generated topologies on groups ........................ 27
10 The characteristic group H(A) of a twin subset A ........... 29
11 Characterizing functions that belong to EndλI(F) ........... 29
12 The H(K)-act TK of a maximal 2-cogroup К ................... 31
13 I-incomparable and I-independent families .................. 33
14 The endomorphism monoid End(TK) of the H(K)-act TK ......... 34
15 The semigroup Endλ(TK) ..................................... 41
16 Constructing nice idempotents in the semigroup
Endλ(P(X)) ................................................. 47
17 The minimal ideal of the semigroups λ(X) and Endλ(P(X)) .... 50
18 Minimal left ideals of superextensions of twinic groups .... 51
19 The structure of the superextensions of abelian groups ..... 58
20 Compact reflexions of groups ............................... 64
21 Some examples .............................................. 66
21.1 The infinite cyclic group  .......................... 66
21.2 The (quasi)cyclic 2-groups C2n ....................... 67
21.3 The groups Q2n of generalized quaternions ............ 68
21.4 The dihedral 2-groups D2n ............................ 70
21.5 Superextensions of finite groups of order < 16 ....... 72
22 Some open problems ......................................... 73
References ..................................................... 74
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